Given an integer n and an array a of length n, your task is to apply the following mutation to a:

• Array a mutates into a new array b of length n.
• For each i from 0 to n - 1, b[i] = a[i - 1] + a[i] + a[i + 1].
• If some element in the sum a[i - 1] + a[i] + a[i + 1] does not exist, it should be set to 0. For example, b[0] should be equal to 0 + a[0] + a[1].

Example

For n = 5 and a = [4, 0, 1, -2, 3], the output should be solution(n, a) = [4, 5, -1, 2, 1].

• b[0] = 0 + a[0] + a[1] = 0 + 4 + 0 = 4
• b[1] = a[0] + a[1] + a[2] = 4 + 0 + 1 = 5
• b[2] = a[1] + a[2] + a[3] = 0 + 1 + (-2) = -1
• b[3] = a[2] + a[3] + a[4] = 1 + (-2) + 3 = 2
• b[4] = a[3] + a[4] + 0 = (-2) + 3 + 0 = 1

So, the resulting array after the mutation will be [4, 5, -1, 2, 1].